We have seen above that the precision measurements of the masses
and the mixings in the sfermion and the chargino/neutralino sector
will certainly allow us to quantitatively test various
supersymmetry relations, thereby firmly establishing
the existence of supersymmetry as a dynamical symmetry
of particle interactions.
More importantly, the precision we expect for these measurements
at the JLC is so high that we will be able to
infer the SUSY breaking scale and
the values of the SUSY breaking parameters at this high scale.
Since these SUSY breaking parameters are presumably determined
by the physics at the high scale,
this will open up a first realistic way to systematically
study the physics at this high scale experimentally.

Some examples of such studies are already mentioned above,
including tests of universality among scalar masses and
gaugino mass unification expected in the SUGRA models.
These tests can be carried out step by step in the course of the
SUSY discovery and study scenarios.
We can hope that, eventually, we will be able to
determine all the masses and the mixings
of the sparticle spectrum,
thereby fixing all of the Lagrangian
parameters such as
at the electroweak (EW) scale.
In this section, we review what and to what extent
we can learn then from these precision
measurements of the masses and the mixings.

One can use these accurately determined Lagrangian parameters
at the EW scale to fit their values at the high scale.
It has been shown [48] in this approach,
that the projected accurate measurements of the
various sparticle masses through an energy scan
for each sparticle's threshold, using
ten energy points with 10
each,
allows one to determine
,
and
at the high scale
to an accuracy better than 12.
The accuracy is much worse, however, for
higher values of
.
The expected accuracy for the trilinear term is rather poor
as shown in Tables 3.5
and 3.6 taken from Ref. [48],
which is due to
the fact that most of
the physical observables are rather insensitive
to the parameters Ak.

In this approach model selection will be made
on the basis of goodness of the fit.

There is, however, a totally different approach to
test the SUSY breaking mechanisms,
the bottom up approach[50],
where one starts with these Lagrangian parameters extracted
at the EW scale and extrapolates them to the high scale
using the renormalization group evolution (RGE).
As explained in Section 3.2,
different SUSY breaking mechanisms predict
different relations among these parameters
at the high scale.
In the bottom up approach,
one can test these relations
directly by reconstructing them
from their low energy values using the RGE.
In Ref.[50],
experimental values of the various sparticle masses
are generated in a given scenario (mSUGRA, GMSB etc.),
by starting from the universal parameters at the high scale
appropriate for the model under consideration
and evolving them down to the EW scale.
These masses are then endowed with experimental errors
expected to be reached eventually in the combined analyses
of data from LHC and a TeV scale linear collider
with an integrated luminosity of
.
These measured values are then evolved
back to the high scale.
The left two plots in Fig. 3.43

Figure 3.43:
Bottom up approach of the determination of the sparticle mass
parameters for mSUGRA and GMSB[50].
Values of the model parameters as given there.

show results of such an exercise for the gaugino
and sfermion masses, respectively, for the mSUGRA case,
while the one on the right for sfermion masses in GMSB.
The width of the bands indicates
C.L. limits.

We can see that with the projected
accuracies of measurements,
the unification of the gaugino masses will be indeed demonstrated
very clearly in the mSUGRA case.
The extrapolation errors for the evolution of the slepton masses
are also small, since only the EW gauge couplings contribute to it,
and allows one to test the unification of the slepton masses
at the high scale.
This is in contrast to the squark and higgs masses,
for which the extrapolation errors are rather large.
In the case of the Higgs mass parameters this insensitivity to
the common scalar mass m0 is due to an accidental cancellation
between different contributions in the loop corrections
to these masses which in turn control the RG evolution.
In the case of the squarks the extrapolation errors
are caused by the stronger dependence of the radiative corrections
on the common gaugino mass,
due to the strong interactions of the squarks.
As a result of these the small error at the EW scale
expands rapidly, when extrapolated to the unification scale.
It should also be noted that
the trilinear A coupling for the top shows a pseudo
fixed point behavior,
which also makes the EW scale value
insensitive to m0.
If the universal gaugino mass m1/2 is larger than the m0
then this pseudo fixed point behavior increases the errors
in the determination of the third generation squark mass
at the EW scale.
This picture shows us clearly the extent to which the unification
at high scale can be tested.
If we compare this with the results of Tables 3.5
and 3.6, we see that with the bottom up approach
we have a much clearer representation of the situation.
It should be stressed that
the
C.L. bands on the squark and the higgs mass parameters
become much wider if one only assumes the accuracies expected
to be reached at the LHC[51].
The linear collider's precision measurements are indispensable to
get a clearer picture of the SUSY breaking mechanism at
the high scale.

The right-most plot in Fig. 3.43
shows the results of a similar
exercise but for the GMSB model,
where with the assumed values of the model parameters,
one would need to have a 1.5 TeV linear collider
to access the full sparticle spectrum.
In this case the doublet slepton mass and the Higgs mass
parameter are expected to unify at the messenger scale,
which the data show quite clearly.
It is remarkable that the extrapolation
of the reconstructed slepton and squark masses
to the high scale is stable enough to reveal the
entirely different unification patterns expected
in this case as opposed to the mSUGRA case.
The bottom up approach of testing the structure
of the SUSY breaking sector definitely requires
the high accuracy that can be achieved only with
the linear collider[51].

All of these discussions assume that most of the sparticle spectrum
are accessible jointly by the LHC and a TeV scale
linear collider.
If we are unlucky and the squarks are super-heavy13,
then perhaps the only clue to their existence
can be obtained through the analogue of precision
measurements of the oblique correction to
the SM parameters at the Z pole.
These super-oblique corrections [53] modify the tree-level
supersymmetry relations between various couplings as already mentioned
in Section 3.3.2.
These modifications arise if there is a large mass splitting between
the sleptons and the squarks.
The expected radiative corrections imply

(3.18)

which amounts to about ,
if the mass splitting is a factor of 10.
We have shown in the previous sections that it might well
be possible to make a measurement with such accuracy at the JLC.